Pseudospectral solution of three-dimensional nonlinear sloshing in a shallow water rectangular tank

Abstract

a b s t r a c tIn this study, a pseudospectral s-transformation model is developed to simulate fully nonlinear sloshing waves in a three-dimensional shallow water rectangular tank. The s-transformation maps the physical domain including the water free surface onto a fixed rectangular computational domain. Chebyshev collocation formulae are used to discretize the governing equation and boundary conditions in the computational domain. The numerical model is validated for three well known analytical and numerical sloshing problems. An extensive study is then made of sloshing in a shallow water tank, and the effects of excitation frequency, base aspect ratio, and amplitude of excitation on the wave motions and patterns are considered. Wave regimes and patterns are considerably influenced by the base aspect ratio. In a shallow water tank with a non-square base, different wave regimes are observed during small-amplitude resonant excitation. Also, bores develop during large amplitude resonance excitation.The present study demonstrates that a pseudospectral s-transformation can accurately model nonlinear sloshing waves in a rectangular tank. Also, results show that contrary to the situation in deeper water tanks, sloshing in shallow water strongly depends on the base aspect ratio.

Effects of base aspect ratio on transient resonant fluid sloshing in a rectangular tank: A numerical study

“…Initial conditions for the velocity potential and free surface elevation (Wu et al, 1998;Chern et al, 2012) are given by φðx; y; z; 0Þ ¼ 0 at z a0;…”

“…Different numerical models are widely applied to the study of free surface motions of liquids undergoing sloshing in tanks. Examples include Faltinsen et al (2003Faltinsen et al ( , 2005Faltinsen et al ( and 2006, Wu and Chen (2009) in both steady state and transient wave motions and Akyildiz et al (1996), Wu et al (1998), Alemi Ardakani and Bridges (2011) and Chern et al (2012) in transient flows.…”

“…Ockendon et al, 1993;Feng and Sethna, 1993;Faltinsen et al, 2006). Recently, Chern et al (2012) examined different base effects on the wave transient sloshing mode (that show the free surface motion in transient condition) in a tank of shallow water depth. Results show that in shallow water containers, the behavior of the sloshing strongly depends on the base aspect ratio.…”

“…A consequence of the mapping is that the free surface cannot be vertical, overturning, or breaking. The present model is an extension of a three-dimensional nonlinear sloshing model by Chern et al (2012). The aim of this work is the numerical study of the effects of base aspect ratio on transient resonant fluid sloshing in different water depths with various excitation directions and amplitudes.…”

A three-dimensional PSME model for rotating flows in an annular cavity

“…Chern et al, 2011). Table 2 lists the parameters used to test for mesh convergence (number of collocation points) and numerical stability (time step).…”